Theorems · Theorem · category theory

CategoryTheory.Limits.image.lift_mk_comp

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y Z : C} (f : X ⟶ Y) (g : Y ⟶ Z)
  [inst_1 : CategoryTheory.Limits.HasImage g]
  [inst_2 : CategoryTheory.Limits.HasImage (CategoryTheory.CategoryStruct.comp f g)]
  (h : Y ⟶ CategoryTheory.Limits.image g)
  (H :
    CategoryTheory.CategoryStruct.comp (CategoryTheory.CategoryStruct.comp f h) (CategoryTheory.Limits.image.ι g) =
      CategoryTheory.CategoryStruct.comp f g),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Limits.image.lift
        { I := CategoryTheory.Limits.image g, m := CategoryTheory.Limits.image.ι g, m_mono := ⋯,
          e := CategoryTheory.CategoryStruct.comp f h, fac := ⋯ })
      (CategoryTheory.Limits.image.ι g) =
    CategoryTheory.Limits.image.ι (CategoryTheory.CategoryStruct.comp f g)

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Images

Cited by

3 results in Mathlib

Foundations

Depth 10 from the axioms · uses propext, Classical.choice

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasImageCategoryTheory.Limits.HasImage